Page 206 - Innovations in Intelligent Machines

198 R.W. Beard
where η p ∼N(0,R)and C = I, and where we have ignored the GPS bias
terms. To implement the extended Kalman filter in Algorithm 2 we need the
Jacobian of f which can be calculated as

⎛ ⎞
00 −V g sin χ
∂f
= ⎝00 V g cos χ ⎠ .
⎟
⎜
∂x
00 0
Figure 10 shows the actual and estimated values for p n , p e ,and χ obtained
by using this scheme. The inaccuracy in the estimates of p n and p e is due to
the GPS bias terms that have been neglected in the system model. Again,
these results are sufficient to enable non-aggressive maneuvers.

7 Summary

Micro air vehicles are increasingly important in both military and civil applica-
tions. The design of intelligent vehicle control software pre-supposes accurate
state estimation techniques. However, the limited computational resources on
board the MAV require computationally simple, yet effective, state estima-
tion algorithms. In this chapter we have derived mathematical models for
the sensors commonly deployed on MAVs. We have also proposed simple
state estimation techniques that have been successfully used in thousands
of hours of actual flight tests using the Procerus Kestrel autopilot (see for
example [7, 6, 21, 10, 17, 18]).

Acknowledgments

This work was partially supported under grants AFOSR grants FA9550-04-1-
0209 and FA9550-04-C-0032 and by NSF award no. CCF-0428004.

References

1. http://www.silicondesigns.com/tech.html.
2. Cloudcap technology. http://www.cloudcaptech.com.
3. Micropilot. http://www.micropilot.com/.
4. Procerus technologies. http://procerusuav.com/.
5. Brian D.O. Anderson and John B. Moore. Optimal Control: Linear Quadratic
Methods. Prentice Hall, Englewood Cliffs, New Jersey, 1990.
6. D. Blake Barber, Stephen R. Griffiths, Timothy W. McLain, and Randal
W. Beard. Autonomous landing of miniature aerial vehicles. In AIAA Infotech@
Aerospace, Arlington, Virginia, September 2005. American Institute of Aeronau-
tics and Astronautics. AIAA-2005-6949.